A pedagogical discussion of the gravitational energy radiated by Keplerian systems

We discuss the use of dimensional analysis and the quadrupolar emission hypothesis to determine the gravitational power radiated by a celestial body in a circular orbit. We then show how to derive the instantaneous power radiated in a general Keplerian orbit by approximating it locally by a circle. This derivation allows us to recover with good accuracy the nontrivial dependence given by general relativity relating the average radiated power to the eccentricity of an ellipse. The approach is understandable by undergraduate students. (C) 2009 American Association of Physics Teachers. [DOI: 10.1119/1.3159610]